What is the derivative of 4arcsin(x^2) ?

The derivative of 4arcsin(x^2) is (8x)/(sqrt(1-x^4))

What is the first derivative of 4arcsin(x^2) ?

The first derivative of 4arcsin(x^2) is (8x)/(sqrt(1-x^4))

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derivative of

4 arcsin (x^{2})

\frac{8 x}{1 - x ^{4}}

Solution steps

\frac{d}{d x} (4 arcsin (x^{2}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (arcsin (x^{2}))

Apply the chain rule:

\frac{1}{1 - ( x ^{2} ) ^{2}} \frac{d}{d x} (x^{2})

= \frac{1}{1 - ( x ^{2} ) ^{2}} \frac{d}{d x} (x^{2})

\frac{d}{d x} (x^{2}) = 2 x

= 4 \cdot \frac{1}{1 - ( x ^{2} ) ^{2}} \cdot 2 x

Simplify

4 \cdot \frac{1}{1 - ( x ^{2} ) ^{2}} \cdot 2 x : \frac{8 x}{1 - x ^{4}}

= \frac{8 x}{1 - x ^{4}}

What is the derivative of 4arcsin(x^2) ?
The derivative of 4arcsin(x^2) is (8x)/(sqrt(1-x^4))
What is the first derivative of 4arcsin(x^2) ?
The first derivative of 4arcsin(x^2) is (8x)/(sqrt(1-x^4))